NDLI: Positive definite solution of a nonlinear matrix equation

Content Provider	Springer Nature Link
Author	Bose, Snehasish Hossein, Sk Mowar Paul, Kallol
Copyright Year	2016
Abstract	Using fixed point theory, we present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation $${X = Q \pm \sum^{m}_{i=1}{A_{i}}^*F(X)A_{i}}$$ , where Q is a positive definite matrix, A $_{ i }$’s are arbitrary n × n matrices and F is a monotone map from the set of positive definite matrices to itself. We show that the presented condition is weaker than that presented by Ran and Reurings [Proc. Amer. Math. Soc. 132 (2004), 1435–1443]. In order to do so, we establish some fixed point theorems for mappings satisfying ( $${\psi, \phi}$$ )-weak contractivity conditions in partially ordered G-metric spaces, which generalize some existing results related to ( $${\psi, \phi}$$ )-weak contractions in partially ordered metric spaces as well as in G-metric spaces for a given function f. We conclude, by presenting an example, that our fixed point theorem cannot be obtained from any existing fixed point theorem using the process of Jleli and Samet [Fixed Point Theory Appl. 2012 (2012), Article ID 210].
Starting Page	627
Ending Page	643
Page Count	17
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	18
Issue Number	3
e-ISSN	16617746
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-05-18
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Matrix equation fixed point weak contraction lower semicontinuous function partially ordered set G-metric space Matrix equations and identities Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. Fixed-point theorems Mathematics Analysis Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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